I know there are the big lists of pets who cannot be obtained as a rare, but what about wild pets? I'm going through different zones doing my battle trainer quests and want to know if there are some that I should pick up when I see them as uncommon if they can't be found as rare.

All wild pets come in rare, it just might take a while to find a rare version of what you're seeking. There are some that have very long respawn timers like Minfernal and Unborn Val'kyr where it would be better to take what you can get rather than hunt for a rare version.

Also some semi rare pets come in tons of breeds so if you care about breeds then sometimes it is leagues easier to farm out the breed you want in any quality and stone it rare. Flayed youngling in s/s breed for example.

My initial strategy when I first started collecting wild pets was to catch one of every single pet first, no matter what rarity it was. Once I had every available wild pet I then when back through the zones and (slowly) replaced them all with rare versions (using upgrade stones of a few as mentioned above).

There used to be three wild pets that only came as uncommon, but that was fixed a long time ago and they now come in all rarities.

These days, I have so many stones that I don't even look at rarity when I go to catch a new wild pet... just the breed. Some pets though, are so rare (as in: hard to find) that I will take whatever I can get.